论文标题
使用不完美测试
Bayesian Beta-Binomial Prevalence Estimation Using an Imperfect Test
论文作者
论文摘要
在[Diggle 2011，Greenland 1995]之后，我们根据人口的不可靠测试为贝叶斯后密度提供了一个简单的公式。当假阳性测试率接近正在测试的人群中的患病率时，此问题尤其重要。提出了一种有效的蒙特卡洛算法，用于近似后密度，并使用[Bendavid 2020]中报道的数据估算了加利福尼亚州圣克拉拉县的COVID-19感染率。我们表明，与48,000---81,000的感染相比，真正的贝叶斯后部将质量更接近零接近零，从而导致5,000--70,000感染（中位数：42,000）（2.17％（95CI 0.27％-3.63％））的患病率估计值（95CI 0.27％-3.63％）），与使用[Bendavid 2020]的48,000---81,000感染相比。 示范可在testprev.com上提供带有代码和其他示例的演示。
Following [Diggle 2011, Greenland 1995], we give a simple formula for the Bayesian posterior density of a prevalence parameter based on unreliable testing of a population. This problem is of particular importance when the false positive test rate is close to the prevalence in the population being tested. An efficient Monte Carlo algorithm for approximating the posterior density is presented, and applied to estimating the Covid-19 infection rate in Santa Clara county, CA using the data reported in [Bendavid 2020]. We show that the true Bayesian posterior places considerably more mass near zero, resulting in a prevalence estimate of 5,000--70,000 infections (median: 42,000) (2.17% (95CI 0.27%--3.63%)), compared to the estimate of 48,000--81,000 infections derived in [Bendavid 2020] using the delta method. A demonstration, with code and additional examples, is available at testprev.com.
